Husharmulga.com Given below are some triangles and lengths of line segments. Identify ray PM is the bisector of ∠QPR. Practice Set 1.2 | Q 1.3 | Page 13

Given below are some triangles and lengths of line segments. Identify ray PM is the bisector of ∠QPR. Practice Set 1.2 | Q 1.3 | Page 13

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Given below are some triangles and lengths of line segments. Identify ray PM is the bisector of ∠QPR.

Practice Set 1.2 | Q 1.3 | Page 13

Given below are some triangles and lengths of line segments. Identify ray PM is the bisector of ∠QPR.

fig1.35
Solution

In ΔQMP,
`"QM"/"QP" = 3.6/9 = 2/5`

In ΔMRP,

`"MR"/"RP" = 4/10 = 2/5`

∴ `"QM"/"QP" = "MR"/"RP"`

By converse of angle bisector theorem, ray PM is the bisector of ∠QPR.

Solution:-

Given:

  • Two triangles QMP and MRP
  • Lengths of line segments: QM = 3.6, QP = 9, MR = 4, RP = 10

To prove: Ray PM is the bisector of ∠QPR.

Proof:

  • "QM"/"QP" = 3.6/9 = 2/5" (Given from triangle QMP)
  • "MR"/"RP" = 4/10 = 2/5" (Given from triangle MRP)
  • "QM"/"QP" = "MR"/"RP" (From the previous two steps)
  • By converse of angle bisector theorem, ray PM is the bisector of ∠QPR.

Chapter 1. Similarity- Practice Set 1.2  – Page 13

Q 1.2
Q 1.3
Q 2

Click Here for All Textbook Soutions of Chapter 1: Similarity